Question

Based on the given information, which equation can be used to find the nth term in the sequence anan​?

A) an=22−4n
B) an=22−2n
C) an=18−4na

Answer 1

To find the nth term in the sequence, analyze the given information and follow the steps. The equation that can be used to find the nth term is an = 2n².

Step-by-step explanation:

To find the nth term in the sequence anan, we can analyze the given information. It states that the expression in the box is equal to n². We can imagine taking (n-1) from the last term and adding it to the first term. This simplifies to 2[n + 3 + .... + (2n-3) + n]. Now, we take (n-3) from the penultimate term and add it to the second term, resulting in 2n². Therefore, the equation that can be used to find the nth term is an = 2n².

Answer 2

Based on the given information, the correct equation to find the nth term in the sequence is:

B)
`\( a_n = 22 - 2n \)`

Step-by-step explanation:

In the given sequence, the general form of the nth term
`(\( a_n \))` is expressed as a function of n . We need to examine the given options and determine which equation correctly represents the pattern in the sequence.

Let's analyze option B,
`\( a_n = 22 - 2n \).` This equation indicates a linear relationship where the term decreases by 2 units with each increase in n . The constant term 22 suggests the initial value of the sequence. To validate this, we can substitute n = 1 and n = 2 into the equation to verify if the sequence follows the given pattern.

For n = 1 ,
`\( a_1 = 22 - 2(1) = 20 \)`. For n = 2 ,
`\( a_2 = 22 - 2(2) = 18 \)`. These values align with the sequence, supporting the correctness of the equation.

Option A,
`\( a_n = 22 - 4n \)`, and option C,
`\( a_n = 18 - 4n \),` do not accurately represent the given sequence as they imply a steeper decrement in values, deviating from the observed pattern. Therefore, the correct choice is option B,
`\( a_n = 22 - 2n \),` which provides a valid equation for finding the nth term in the sequence.